Wet-running double-clutch arrangements are previously known in a plurality of versions from the existing art. These have one input and two outputs, the input being formed of a driver unit, which is connected to a first clutch part of each of the individual clutch arrangements of the wet-running double clutch. Each clutch arrangement has a second clutch part, which may be brought into operative connection with the first clutch part and is coupled with the output in a rotationally fixed connection. Such clutch designs are frequently of multi-disk or lamellar construction, so that the first clutch part is formed of a first lamellar array and the second clutch part is formed of a second lamellar array, where the two lamellar arrays may be brought into a frictionally engaged operative connection with each other by means of an actuating device, usually in the form of a piston element actuated by a pressurizing agent. To that end, each of the clutch arrangements has its own actuating device, preferably in the form of a piston element. Assigned to the piston element for actuation is at least one chamber pressurizable with a pressurizing agent, but preferably two chambers pressurizable with a pressurizing agent, which act on the two faces of the piston element directed away from each other, and where a first of the chambers pressurizable with a pressurizing agent serves directly as a pressure chamber for operating the piston, and the second chamber assigned to a piston element serves as a compensating chamber. The chambers are connected to a pressurizing agent supply and conducting system, with the individual chambers assigned to a piston element being separately addressable. The contact force of the piston can be set by means of the pressure difference in the two chambers. Because of the wet operation of the lamella, which are always running in oil, the chambers which are pressurizable with a pressurizing agent must be separated from the interior space of the wet-running double clutch. The individual clutch arrangements are situated coaxially to each other and one inside the other in the radial direction, and preferably with little or no offset in relation to each other in the axial direction. The sealing of the individual chambers in relation to the interior space or to each other is accomplished by means of sealing arrangements comprising elastic sealing devices, these being moving sealing devices in this case, since they usually seal the piston in relation to a stationary component, and the sealing surface is moved along with the motion of the piston. The sealing arrangements are therefore normally vulcanized directly onto the piston element, or to an element that is frictionally connected thereto. This means that to apply the sealing device, the entire piston element—and thus a relatively large component which in some versions has a cross section with complex geometry—must be handled and subjected to the vulcanizing process. The geometry of the piston determines both the arrangement of the sealing device and the arrangement and form of the other surface areas of the chamber pressurizable with a pressurizing agent which are to be brought into operative connection with the sealing device. Highly precise fabrication is therefore necessary to realize a reliable sealing function. Furthermore, if the sealing surfaces are damaged there is no simple means of replacing the individual sealing devices.